HS614 HW#3
Tiffany Chua
getwd()## [1] "/Users/tiffa.chua/Desktop/HS614/HS614_Data-Analysis"HS614: Homework #3
For this HW use the diabetes dataset.
Exploratory Data Analysis: 1. Explore the data 2. How many rows and columns? 3. Any NAs? If yes, which columns? 4. Any strange values? If yes, what to do? 5. Any correlation between features? 6. Statistics of the columns and some exploratory plots (bar plot, histogram, boxplot …)
Build at least 4 different predictive models that can predict (classify) Diabetic patients. Compare the performance of the models.
Column definitions of this dataset are given in table 1 of this paper: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8306487/
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library(corrplot)
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## marginlibrary(animation)diab <- read.csv("./diabetes.csv")
head(diab)## Pregnancies Glucose BloodPressure SkinThickness Insulin BMI
## 1 6 148 72 35 0 33.6
## 2 1 85 66 29 0 26.6
## 3 8 183 64 0 0 23.3
## 4 1 89 66 23 94 28.1
## 5 0 137 40 35 168 43.1
## 6 5 116 74 0 0 25.6
## DiabetesPedigreeFunction Age Outcome
## 1 0.627 50 1
## 2 0.351 31 0
## 3 0.672 32 1
## 4 0.167 21 0
## 5 2.288 33 1
## 6 0.201 30 0str(diab)## 'data.frame': 768 obs. of 9 variables:
## $ Pregnancies : int 6 1 8 1 0 5 3 10 2 8 ...
## $ Glucose : int 148 85 183 89 137 116 78 115 197 125 ...
## $ BloodPressure : int 72 66 64 66 40 74 50 0 70 96 ...
## $ SkinThickness : int 35 29 0 23 35 0 32 0 45 0 ...
## $ Insulin : int 0 0 0 94 168 0 88 0 543 0 ...
## $ BMI : num 33.6 26.6 23.3 28.1 43.1 25.6 31 35.3 30.5 0 ...
## $ DiabetesPedigreeFunction: num 0.627 0.351 0.672 0.167 2.288 ...
## $ Age : int 50 31 32 21 33 30 26 29 53 54 ...
## $ Outcome : int 1 0 1 0 1 0 1 0 1 1 ...Variable Definitions
- Pregnancy - Frequency of pregnancy
- Glucose - Concentration of plasma glucose (mg/dL)
- BP - Diastolic blood pressure (mmHg)
- Skin - Tricep skinfold thickness (mm)
- Insulin - Two-hour serum insulin (mu U/ml)
- BMI - Body mass index (kg/m2)
- Pedigree - A pedigree function for diabetes
- Age - Age (log(years))
diab$Outcome = factor(diab$Outcome)
str(diab)## 'data.frame': 768 obs. of 9 variables:
## $ Pregnancies : int 6 1 8 1 0 5 3 10 2 8 ...
## $ Glucose : int 148 85 183 89 137 116 78 115 197 125 ...
## $ BloodPressure : int 72 66 64 66 40 74 50 0 70 96 ...
## $ SkinThickness : int 35 29 0 23 35 0 32 0 45 0 ...
## $ Insulin : int 0 0 0 94 168 0 88 0 543 0 ...
## $ BMI : num 33.6 26.6 23.3 28.1 43.1 25.6 31 35.3 30.5 0 ...
## $ DiabetesPedigreeFunction: num 0.627 0.351 0.672 0.167 2.288 ...
## $ Age : int 50 31 32 21 33 30 26 29 53 54 ...
## $ Outcome : Factor w/ 2 levels "0","1": 2 1 2 1 2 1 2 1 2 2 ...table(diab$Outcome)##
## 0 1
## 500 268Rows & Columns
nrow(diab)## [1] 768ncol(diab)## [1] 9Missing & Strange Variables
sum(is.na(diab))## [1] 0missmap(diab)
#Note: While there are no NA variables, missing data points seem to have been replaced with a value of 0 in columnsNote: While there are no NA variables, missing data points seem to have been replaced with a value of 0 in columns.
sum(diab$Glucose == 0)## [1] 5sum(diab$BloodPressure == 0)## [1] 35sum(diab$SkinThickness == 0)## [1] 227sum(diab$Insulin == 0)## [1] 374sum(diab$BMI == 0)## [1] 11sum(diab$DiabetesPedigreeFunction == 0)## [1] 0sum(diab$Age == 0)## [1] 0#Strange Values:
#The following columns returned values of 0 Glucose, BloodPressure, SkinThickness, Insulin, and BMI; It is likely that missing/NA variables for these columns were replaced with 0, as 0 is a highly unlikely and unrealistic observation for these featuresStrange Values The following columns returned values of 0: Glucose, BloodPressure, SkinThickness, Insulin, and BMI. It is likely that missing/NA variables for these columns were replaced with 0, as 0 is a highly unlikely and unrealistic observation for these features.
#What to do with the strange values?
diab1 <- diab
#Turn strange (0) values into NA
diab1$Glucose[diab1$Glucose == 0] = NA
diab1$BloodPressure[diab1$BloodPressure == 0] = NA
diab1$SkinThickness[diab1$SkinThickness == 0] = NA
diab1$Insulin[diab1$Insulin == 0] = NA
diab1$BMI[diab1$BMI == 0] = NA
sum(is.na(diab1))## [1] 652missmap(diab1)
#I will use mean imputation on the NA variables in the Predictive Models section (after Train/Test Split)What to do with the strange variables? 1. Turn strange (0) values into NA. 2. I will use mean imputation on the NA variables in the Predicive Models section (after Train/Test Split).
Exploratory Data Analysis
Initial Read
Descriptive Statistics
stat.desc(diab1)## Pregnancies Glucose BloodPressure SkinThickness Insulin
## nbr.val 768.0000000 7.630000e+02 7.330000e+02 5.410000e+02 3.940000e+02
## nbr.null 111.0000000 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## nbr.na 0.0000000 5.000000e+00 3.500000e+01 2.270000e+02 3.740000e+02
## min 0.0000000 4.400000e+01 2.400000e+01 7.000000e+00 1.400000e+01
## max 17.0000000 1.990000e+02 1.220000e+02 9.900000e+01 8.460000e+02
## range 17.0000000 1.550000e+02 9.800000e+01 9.200000e+01 8.320000e+02
## sum 2953.0000000 9.284700e+04 5.307300e+04 1.577200e+04 6.128600e+04
## median 3.0000000 1.170000e+02 7.200000e+01 2.900000e+01 1.250000e+02
## mean 3.8450521 1.216868e+02 7.240518e+01 2.915342e+01 1.555482e+02
## SE.mean 0.1215892 1.105464e+00 4.573454e-01 4.504407e-01 5.983841e+00
## CI.mean.0.95 0.2386871 2.170117e+00 8.978652e-01 8.848307e-01 1.176434e+01
## var 11.3540563 9.324254e+02 1.533178e+02 1.097672e+02 1.410770e+04
## std.dev 3.3695781 3.053564e+01 1.238216e+01 1.047698e+01 1.187759e+02
## coef.var 0.8763413 2.509364e-01 1.710120e-01 3.593740e-01 7.635951e-01
## BMI DiabetesPedigreeFunction Age Outcome
## nbr.val 7.570000e+02 768.00000000 7.680000e+02 NA
## nbr.null 0.000000e+00 0.00000000 0.000000e+00 NA
## nbr.na 1.100000e+01 0.00000000 0.000000e+00 NA
## min 1.820000e+01 0.07800000 2.100000e+01 NA
## max 6.710000e+01 2.42000000 8.100000e+01 NA
## range 4.890000e+01 2.34200000 6.000000e+01 NA
## sum 2.457030e+04 362.40100000 2.552900e+04 NA
## median 3.230000e+01 0.37250000 2.900000e+01 NA
## mean 3.245746e+01 0.47187630 3.324089e+01 NA
## SE.mean 2.516930e-01 0.01195579 4.243608e-01 NA
## CI.mean.0.95 4.941002e-01 0.02346996 8.330464e-01 NA
## var 4.795546e+01 0.10977864 1.383030e+02 NA
## std.dev 6.924988e+00 0.33132860 1.176023e+01 NA
## coef.var 2.133558e-01 0.70215138 3.537882e-01 NAsummary(diab1)## Pregnancies Glucose BloodPressure SkinThickness
## Min. : 0.000 Min. : 44.0 Min. : 24.00 Min. : 7.00
## 1st Qu.: 1.000 1st Qu.: 99.0 1st Qu.: 64.00 1st Qu.:22.00
## Median : 3.000 Median :117.0 Median : 72.00 Median :29.00
## Mean : 3.845 Mean :121.7 Mean : 72.41 Mean :29.15
## 3rd Qu.: 6.000 3rd Qu.:141.0 3rd Qu.: 80.00 3rd Qu.:36.00
## Max. :17.000 Max. :199.0 Max. :122.00 Max. :99.00
## NA's :5 NA's :35 NA's :227
## Insulin BMI DiabetesPedigreeFunction Age
## Min. : 14.00 Min. :18.20 Min. :0.0780 Min. :21.00
## 1st Qu.: 76.25 1st Qu.:27.50 1st Qu.:0.2437 1st Qu.:24.00
## Median :125.00 Median :32.30 Median :0.3725 Median :29.00
## Mean :155.55 Mean :32.46 Mean :0.4719 Mean :33.24
## 3rd Qu.:190.00 3rd Qu.:36.60 3rd Qu.:0.6262 3rd Qu.:41.00
## Max. :846.00 Max. :67.10 Max. :2.4200 Max. :81.00
## NA's :374 NA's :11
## Outcome
## 0:500
## 1:268
##
##
##
##
## Correlations
diab_num <- diab1[1:8]
M <- cor(diab_num,
method = "pearson")
M## Pregnancies Glucose BloodPressure SkinThickness
## Pregnancies 1.00000000 NA NA NA
## Glucose NA 1 NA NA
## BloodPressure NA NA 1 NA
## SkinThickness NA NA NA 1
## Insulin NA NA NA NA
## BMI NA NA NA NA
## DiabetesPedigreeFunction -0.03352267 NA NA NA
## Age 0.54434123 NA NA NA
## Insulin BMI DiabetesPedigreeFunction Age
## Pregnancies NA NA -0.03352267 0.54434123
## Glucose NA NA NA NA
## BloodPressure NA NA NA NA
## SkinThickness NA NA NA NA
## Insulin 1 NA NA NA
## BMI NA 1 NA NA
## DiabetesPedigreeFunction NA NA 1.00000000 0.03356131
## Age NA NA 0.03356131 1.00000000corrplot(M,
method = "square")
cor.plot(diab_num)
#Highest Correlating Variables:
# BMI & SkinThickness = 0.65
# Insulin & Glucose = 0.58
# Pregnancies & Age = 0.54
# BloodPressure & Age = 0.33
# BMI & BloodPressure = 0.29Highest Correlating Variables: * BMI & SkinThickness = 0.65 * Insulin & Glucose = 0.58 * Pregnancies & Age = 0.54 * BloodPressure & Age = 0.33 * BMI & BloodPressure = 0.29
Plots
ggpairs(diab1)## Warning in ggally_statistic(data = data, mapping = mapping, na.rm = na.rm, :
## Removed 5 rows containing missing values## Warning in ggally_statistic(data = data, mapping = mapping, na.rm = na.rm, :
## Removed 35 rows containing missing values## Warning in ggally_statistic(data = data, mapping = mapping, na.rm = na.rm, :
## Removed 227 rows containing missing values## Warning in ggally_statistic(data = data, mapping = mapping, na.rm = na.rm, :
## Removed 374 rows containing missing values## Warning in ggally_statistic(data = data, mapping = mapping, na.rm = na.rm, :
## Removed 11 rows containing missing values## Warning: Removed 5 rows containing missing values (geom_point).## Warning: Removed 5 rows containing non-finite values (stat_density).## Warning in ggally_statistic(data = data, mapping = mapping, na.rm = na.rm, :
## Removed 40 rows containing missing values## Warning in ggally_statistic(data = data, mapping = mapping, na.rm = na.rm, :
## Removed 232 rows containing missing values## Warning in ggally_statistic(data = data, mapping = mapping, na.rm = na.rm, :
## Removed 375 rows containing missing values## Warning in ggally_statistic(data = data, mapping = mapping, na.rm = na.rm, :
## Removed 16 rows containing missing values## Warning in ggally_statistic(data = data, mapping = mapping, na.rm = na.rm, :
## Removed 5 rows containing missing values
## Warning in ggally_statistic(data = data, mapping = mapping, na.rm = na.rm, :
## Removed 5 rows containing missing values## Warning: Removed 5 rows containing non-finite values (stat_boxplot).## Warning: Removed 35 rows containing missing values (geom_point).## Warning: Removed 40 rows containing missing values (geom_point).## Warning: Removed 35 rows containing non-finite values (stat_density).## Warning in ggally_statistic(data = data, mapping = mapping, na.rm = na.rm, :
## Removed 229 rows containing missing values## Warning in ggally_statistic(data = data, mapping = mapping, na.rm = na.rm, :
## Removed 374 rows containing missing values## Warning in ggally_statistic(data = data, mapping = mapping, na.rm = na.rm, :
## Removed 39 rows containing missing values## Warning in ggally_statistic(data = data, mapping = mapping, na.rm = na.rm, :
## Removed 35 rows containing missing values
## Warning in ggally_statistic(data = data, mapping = mapping, na.rm = na.rm, :
## Removed 35 rows containing missing values## Warning: Removed 35 rows containing non-finite values (stat_boxplot).## Warning: Removed 227 rows containing missing values (geom_point).## Warning: Removed 232 rows containing missing values (geom_point).## Warning: Removed 229 rows containing missing values (geom_point).## Warning: Removed 227 rows containing non-finite values (stat_density).## Warning in ggally_statistic(data = data, mapping = mapping, na.rm = na.rm, :
## Removed 374 rows containing missing values## Warning in ggally_statistic(data = data, mapping = mapping, na.rm = na.rm, :
## Removed 229 rows containing missing values## Warning in ggally_statistic(data = data, mapping = mapping, na.rm = na.rm, :
## Removed 227 rows containing missing values
## Warning in ggally_statistic(data = data, mapping = mapping, na.rm = na.rm, :
## Removed 227 rows containing missing values## Warning: Removed 227 rows containing non-finite values (stat_boxplot).## Warning: Removed 374 rows containing missing values (geom_point).## Warning: Removed 375 rows containing missing values (geom_point).## Warning: Removed 374 rows containing missing values (geom_point).
## Warning: Removed 374 rows containing missing values (geom_point).## Warning: Removed 374 rows containing non-finite values (stat_density).## Warning in ggally_statistic(data = data, mapping = mapping, na.rm = na.rm, :
## Removed 375 rows containing missing values## Warning in ggally_statistic(data = data, mapping = mapping, na.rm = na.rm, :
## Removed 374 rows containing missing values
## Warning in ggally_statistic(data = data, mapping = mapping, na.rm = na.rm, :
## Removed 374 rows containing missing values## Warning: Removed 374 rows containing non-finite values (stat_boxplot).## Warning: Removed 11 rows containing missing values (geom_point).## Warning: Removed 16 rows containing missing values (geom_point).## Warning: Removed 39 rows containing missing values (geom_point).## Warning: Removed 229 rows containing missing values (geom_point).## Warning: Removed 375 rows containing missing values (geom_point).## Warning: Removed 11 rows containing non-finite values (stat_density).## Warning in ggally_statistic(data = data, mapping = mapping, na.rm = na.rm, :
## Removed 11 rows containing missing values
## Warning in ggally_statistic(data = data, mapping = mapping, na.rm = na.rm, :
## Removed 11 rows containing missing values## Warning: Removed 11 rows containing non-finite values (stat_boxplot).## Warning: Removed 5 rows containing missing values (geom_point).## Warning: Removed 35 rows containing missing values (geom_point).## Warning: Removed 227 rows containing missing values (geom_point).## Warning: Removed 374 rows containing missing values (geom_point).## Warning: Removed 11 rows containing missing values (geom_point).## Warning: Removed 5 rows containing missing values (geom_point).## Warning: Removed 35 rows containing missing values (geom_point).## Warning: Removed 227 rows containing missing values (geom_point).## Warning: Removed 374 rows containing missing values (geom_point).## Warning: Removed 11 rows containing missing values (geom_point).## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.## Warning: Removed 5 rows containing non-finite values (stat_bin).## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.## Warning: Removed 35 rows containing non-finite values (stat_bin).## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.## Warning: Removed 227 rows containing non-finite values (stat_bin).## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.## Warning: Removed 374 rows containing non-finite values (stat_bin).## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.## Warning: Removed 11 rows containing non-finite values (stat_bin).## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
Outcome Barplot
ggplot(diab1,
aes(Outcome)) +
geom_bar()
Histograms, grouped by Outcome
# Grouped
# p <- data %>%
# ggplot( aes(x=value, fill=type)) +
# geom_histogram( color="#e9ecef", alpha=0.6, position = 'identity') +
# scale_fill_manual(values=c("#69b3a2", "#404080")) +
# theme_ipsum() +
# labs(fill="")
Glucose_hist <- diab1 %>%
ggplot(aes(x = Glucose,
fill = Outcome)) +
geom_histogram(binwidth = 5)
Glucose_hist## Warning: Removed 5 rows containing non-finite values (stat_bin).
BP_hist <- diab1 %>%
ggplot(aes(x = BloodPressure,
fill = Outcome)) +
geom_histogram(binwidth = 5)
BP_hist## Warning: Removed 35 rows containing non-finite values (stat_bin).
BMI_hist <- diab1 %>%
ggplot(aes(x = BMI,
fill = Outcome)) +
geom_histogram(binwidth = 2)
BMI_hist## Warning: Removed 11 rows containing non-finite values (stat_bin).
Ped_hist <- diab1 %>%
ggplot(aes(x = DiabetesPedigreeFunction,
fill = Outcome)) +
geom_histogram(binwidth = 0.075)
Ped_hist
Age_hist <- diab1 %>%
ggplot(aes(x = Age,
fill = Outcome)) +
geom_histogram(binwidth = 2)
Age_hist
Scatter Plots, grouped by Outcome
#Highest Correlating Variables:
# BMI & SkinThickness = 0.65
# Insulin & Glucose = 0.58
# Pregnancies & Age = 0.54
# BloodPressure & Age = 0.33
# BMI & BloodPressure = 0.29
# BMI & SkinThickness = 0.65
BMI_Skin <- ggplot(data = diab1,
aes(x = BMI,
y = SkinThickness,
color = Outcome),
na.rm = TRUE) +
geom_point(size = 0.5) +
geom_smooth(method = lm) +
labs(title = "BMI vs. Skin Thickness")
BMI_Skin## `geom_smooth()` using formula 'y ~ x'## Warning: Removed 229 rows containing non-finite values (stat_smooth).## Warning: Removed 229 rows containing missing values (geom_point).
# Insulin & Glucose = 0.58
Insu_Glucose <- ggplot(data = diab1,
aes(x = Insulin,
y = Glucose,
color = Outcome),
na.rm = TRUE) +
geom_point(size = 0.5) +
geom_smooth(method = lm) +
labs(title = "Insulin vs. Glucose")
Insu_Glucose## `geom_smooth()` using formula 'y ~ x'## Warning: Removed 375 rows containing non-finite values (stat_smooth).## Warning: Removed 375 rows containing missing values (geom_point).
# Pregnancies & Age = 0.54
Age_Preg <- ggplot(data = diab1,
aes(x = Age,
y = Pregnancies,
color = Outcome),
na.rm = TRUE) +
geom_point(size = 0.5) +
geom_smooth(method = lm) +
labs(title = "Age vs. Pregnancies")
Age_Preg## `geom_smooth()` using formula 'y ~ x'
# BloodPressure & Age = 0.33
Age_BP <- ggplot(data = diab1,
aes(x = Age,
y = BloodPressure,
color = Outcome),
na.rm = TRUE) +
geom_point(size = 0.5) +
geom_smooth(method = lm) +
labs(title = "Age vs. Blood Pressure")
Age_BP## `geom_smooth()` using formula 'y ~ x'## Warning: Removed 35 rows containing non-finite values (stat_smooth).## Warning: Removed 35 rows containing missing values (geom_point).
# Glucose & Age = 0.32
Age_Glucose <- ggplot(data = diab1,
aes(x = Age,
y = Glucose,
color = Outcome),
na.rm = TRUE) +
geom_point(size = 0.5) +
geom_smooth(method = lm) +
labs(title = "Age vs. Glucose")
Age_Glucose## `geom_smooth()` using formula 'y ~ x'## Warning: Removed 5 rows containing non-finite values (stat_smooth).## Warning: Removed 5 rows containing missing values (geom_point).
# BloodPressure & BMI = 0.29
BMI_BP <- ggplot(data = diab1,
aes(x = BMI,
y = BloodPressure,
color = Outcome),
na.rm = TRUE) +
geom_point(size = 0.5) +
geom_smooth(method = lm) +
labs(title = "BMI vs. Blood Pressure")
BMI_BP## `geom_smooth()` using formula 'y ~ x'## Warning: Removed 39 rows containing non-finite values (stat_smooth).## Warning: Removed 39 rows containing missing values (geom_point).
Predictive Models
Train & Test Split
set.seed(123)
split <- sample.split(diab1$Outcome,
SplitRatio = 0.8)
diab.train <- subset(diab1,
split == TRUE)
diab.test <- subset(subset(diab1,
split == FALSE))
nrow(diab.test)## [1] 154nrow(diab.train)## [1] 614head(diab.train)## Pregnancies Glucose BloodPressure SkinThickness Insulin BMI
## 1 6 148 72 35 NA 33.6
## 2 1 85 66 29 NA 26.6
## 3 8 183 64 NA NA 23.3
## 4 1 89 66 23 94 28.1
## 5 0 137 40 35 168 43.1
## 8 10 115 NA NA NA 35.3
## DiabetesPedigreeFunction Age Outcome
## 1 0.627 50 1
## 2 0.351 31 0
## 3 0.672 32 1
## 4 0.167 21 0
## 5 2.288 33 1
## 8 0.134 29 0str(diab.train)## 'data.frame': 614 obs. of 9 variables:
## $ Pregnancies : int 6 1 8 1 0 10 8 4 10 10 ...
## $ Glucose : int 148 85 183 89 137 115 125 110 168 139 ...
## $ BloodPressure : int 72 66 64 66 40 NA 96 92 74 80 ...
## $ SkinThickness : int 35 29 NA 23 35 NA NA NA NA NA ...
## $ Insulin : int NA NA NA 94 168 NA NA NA NA NA ...
## $ BMI : num 33.6 26.6 23.3 28.1 43.1 35.3 NA 37.6 38 27.1 ...
## $ DiabetesPedigreeFunction: num 0.627 0.351 0.672 0.167 2.288 ...
## $ Age : int 50 31 32 21 33 29 54 30 34 57 ...
## $ Outcome : Factor w/ 2 levels "0","1": 2 1 2 1 2 1 2 1 2 1 ...nrow(diab.train)## [1] 614ncol(diab.train)## [1] 9sum(is.na(diab.train))## [1] 536sum(is.na(diab.test))## [1] 116diab.train$Glucose[is.na(diab.train$Glucose)] <- mean(diab.train$Glucose,
na.rm = TRUE)
diab.train$BloodPressure[is.na(diab.train$BloodPressure)] <- mean(diab.train$BloodPressure,
na.rm = TRUE)
diab.train$SkinThickness[is.na(diab.train$SkinThickness)] <- mean(diab.train$SkinThickness,
na.rm = TRUE)
diab.train$Insulin[is.na(diab.train$Insulin)] <- mean(diab.train$Insulin,
na.rm = TRUE)
diab.train$BMI[is.na(diab.train$BMI)] <- mean(diab.train$BMI,
na.rm = TRUE)
sum(is.na(diab.train))## [1] 0str(diab.train)## 'data.frame': 614 obs. of 9 variables:
## $ Pregnancies : int 6 1 8 1 0 10 8 4 10 10 ...
## $ Glucose : num 148 85 183 89 137 115 125 110 168 139 ...
## $ BloodPressure : num 72 66 64 66 40 ...
## $ SkinThickness : num 35 29 29.2 23 35 ...
## $ Insulin : num 154 154 154 94 168 ...
## $ BMI : num 33.6 26.6 23.3 28.1 43.1 ...
## $ DiabetesPedigreeFunction: num 0.627 0.351 0.672 0.167 2.288 ...
## $ Age : int 50 31 32 21 33 29 54 30 34 57 ...
## $ Outcome : Factor w/ 2 levels "0","1": 2 1 2 1 2 1 2 1 2 1 ...diab.test$Glucose[is.na(diab.test$Glucose)] <- mean(diab.train$Glucose,
na.rm = TRUE)
diab.test$BloodPressure[is.na(diab.test$BloodPressure)] <- mean(diab.train$BloodPressure,
na.rm = TRUE)
diab.test$SkinThickness[is.na(diab.test$SkinThickness)] <- mean(diab.train$SkinThickness,
na.rm = TRUE)
diab.test$Insulin[is.na(diab.test$Insulin)] <- mean(diab.train$Insulin,
na.rm = TRUE)
diab.test$BMI[is.na(diab.test$BMI)] <- mean(diab.train$BMI,
na.rm = TRUE)
sum(is.na(diab.test))## [1] 0head(diab.test)## Pregnancies Glucose BloodPressure SkinThickness Insulin BMI
## 6 5 116 74 29.17647 154.3137 25.6
## 7 3 78 50 32.00000 88.0000 31.0
## 9 2 197 70 45.00000 543.0000 30.5
## 14 1 189 60 23.00000 846.0000 30.1
## 17 0 118 84 47.00000 230.0000 45.8
## 22 8 99 84 29.17647 154.3137 35.4
## DiabetesPedigreeFunction Age Outcome
## 6 0.201 30 0
## 7 0.248 26 1
## 9 0.158 53 1
## 14 0.398 59 1
## 17 0.551 31 1
## 22 0.388 50 0Logistic Regression
Logistic Regression Models
logModel1 <- glm(formula = Outcome ~ . ,
family = binomial,
data = diab.train)
summary(logModel1)##
## Call:
## glm(formula = Outcome ~ ., family = binomial, data = diab.train)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.5108 -0.7124 -0.3915 0.6682 2.1827
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -8.799113 0.892047 -9.864 < 2e-16 ***
## Pregnancies 0.135168 0.037465 3.608 0.000309 ***
## Glucose 0.040167 0.004477 8.972 < 2e-16 ***
## BloodPressure -0.015105 0.009399 -1.607 0.108045
## SkinThickness 0.005799 0.015364 0.377 0.705834
## Insulin -0.002570 0.001424 -1.805 0.071029 .
## BMI 0.096264 0.020274 4.748 2.05e-06 ***
## DiabetesPedigreeFunction 0.559306 0.337462 1.657 0.097441 .
## Age 0.014412 0.010702 1.347 0.178086
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 793.94 on 613 degrees of freedom
## Residual deviance: 564.46 on 605 degrees of freedom
## AIC: 582.46
##
## Number of Fisher Scoring iterations: 5#Based on logModel1, the significant values are as follows:
# ***: Glucose
# *: BMI
# .: Insulin
#AIC: 284.17Based on logModel1, the significant values are as follows: * **: Glucose : BMI .: Insulin
AIC: 284.17
logModel2 <- glm(formula = Outcome ~ Glucose + BMI + Insulin,
family = binomial,
data = diab.train)
summary(logModel2)##
## Call:
## glm(formula = Outcome ~ Glucose + BMI + Insulin, family = binomial,
## data = diab.train)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.2588 -0.7506 -0.4374 0.7348 2.3611
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -8.339728 0.733854 -11.364 <2e-16 ***
## Glucose 0.041933 0.004311 9.728 <2e-16 ***
## BMI 0.085804 0.016109 5.326 1e-07 ***
## Insulin -0.002365 0.001381 -1.713 0.0868 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 793.94 on 613 degrees of freedom
## Residual deviance: 595.13 on 610 degrees of freedom
## AIC: 603.13
##
## Number of Fisher Scoring iterations: 4#Based on logModel2, the significant values are as follows:
# ***: Glucose, BMI
# .: Insulin
#AIC: 289.49
#Because this AIC is higher than for logModel1 (289.49 > 284.17), we can assume that logModel1 is better than logModel2Based on logModel2, the significant values are as follows: * **: Glucose, BMI .: Insulin
AIC: 289.49 Because this AIC is higher than for logModel1 (289.49 > 284.17), we can assume that logModel1 is better than logModel2.
logModel3 <- glm(formula = Outcome ~ Glucose + BMI,
family = binomial,
data = diab.train)
summary(logModel3)##
## Call:
## glm(formula = Outcome ~ Glucose + BMI, family = binomial, data = diab.train)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.2748 -0.7531 -0.4407 0.7271 2.2838
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -8.235682 0.723816 -11.378 < 2e-16 ***
## Glucose 0.039075 0.003874 10.086 < 2e-16 ***
## BMI 0.082170 0.015837 5.189 2.12e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 793.94 on 613 degrees of freedom
## Residual deviance: 597.95 on 611 degrees of freedom
## AIC: 603.95
##
## Number of Fisher Scoring iterations: 4#Based on logModel3, the significant values are as follows:
# ***: Glucose, BMI
#AIC: 590.81
#Because this AIC is higher than for logModel1 and logModel2 (590.81 > 289.49 > 284.17), we can assume that this model is not as good as logModel1 or logModel2Based on logModel3, the significant values are as follows: * ***: Glucose, BMI
AIC: 590.81 Because this AIC is higher than for logModel1 and logModel2 (590.81 > 289.49 > 284.17), we can assume that this model is not as good as logModel1 or logModel2.
Logistic Regression Prediction
Outcome.predictions <- predict(logModel1,
diab.test,
type = "response")
log.results <- cbind(Outcome.predictions,
diab.test$Outcome)
results.class <- ifelse(log.results > 0.5, 1,0)
colnames(results.class) <- c("pred", "real")
results.class <- as.data.frame(results.class)
head(results.class)## pred real
## 6 0 1
## 7 0 1
## 9 1 1
## 14 0 1
## 17 0 1
## 22 0 1Logistic Regression Confusion Matrix
table(diab.test$Outcome,
results.class$pred)##
## 0 1
## 0 84 16
## 1 24 30K-Nearest Neighbor
head(diab.train)## Pregnancies Glucose BloodPressure SkinThickness Insulin BMI
## 1 6 148 72.00000 35.00000 154.3137 33.6
## 2 1 85 66.00000 29.00000 154.3137 26.6
## 3 8 183 64.00000 29.17647 154.3137 23.3
## 4 1 89 66.00000 23.00000 94.0000 28.1
## 5 0 137 40.00000 35.00000 168.0000 43.1
## 8 10 115 72.43027 29.17647 154.3137 35.3
## DiabetesPedigreeFunction Age Outcome
## 1 0.627 50 1
## 2 0.351 31 0
## 3 0.672 32 1
## 4 0.167 21 0
## 5 2.288 33 1
## 8 0.134 29 0head(diab.test)## Pregnancies Glucose BloodPressure SkinThickness Insulin BMI
## 6 5 116 74 29.17647 154.3137 25.6
## 7 3 78 50 32.00000 88.0000 31.0
## 9 2 197 70 45.00000 543.0000 30.5
## 14 1 189 60 23.00000 846.0000 30.1
## 17 0 118 84 47.00000 230.0000 45.8
## 22 8 99 84 29.17647 154.3137 35.4
## DiabetesPedigreeFunction Age Outcome
## 6 0.201 30 0
## 7 0.248 26 1
## 9 0.158 53 1
## 14 0.398 59 1
## 17 0.551 31 1
## 22 0.388 50 0str(diab.train)## 'data.frame': 614 obs. of 9 variables:
## $ Pregnancies : int 6 1 8 1 0 10 8 4 10 10 ...
## $ Glucose : num 148 85 183 89 137 115 125 110 168 139 ...
## $ BloodPressure : num 72 66 64 66 40 ...
## $ SkinThickness : num 35 29 29.2 23 35 ...
## $ Insulin : num 154 154 154 94 168 ...
## $ BMI : num 33.6 26.6 23.3 28.1 43.1 ...
## $ DiabetesPedigreeFunction: num 0.627 0.351 0.672 0.167 2.288 ...
## $ Age : int 50 31 32 21 33 29 54 30 34 57 ...
## $ Outcome : Factor w/ 2 levels "0","1": 2 1 2 1 2 1 2 1 2 1 ...str(diab.test)## 'data.frame': 154 obs. of 9 variables:
## $ Pregnancies : int 5 3 2 1 0 8 11 9 2 0 ...
## $ Glucose : num 116 78 197 189 118 99 143 102 90 180 ...
## $ BloodPressure : num 74 50 70 60 84 84 94 76 68 66 ...
## $ SkinThickness : num 29.2 32 45 23 47 ...
## $ Insulin : num 154 88 543 846 230 ...
## $ BMI : num 25.6 31 30.5 30.1 45.8 35.4 36.6 32.9 38.2 42 ...
## $ DiabetesPedigreeFunction: num 0.201 0.248 0.158 0.398 0.551 ...
## $ Age : int 30 26 53 59 31 50 51 46 27 25 ...
## $ Outcome : Factor w/ 2 levels "0","1": 1 2 2 2 2 1 2 2 2 2 ...sum(is.na(diab.train))## [1] 0sum(is.na(diab.test))## [1] 0KNN Fitting
#Fitting K-NN to the Training set and Predicting the Test set results
vec = c()
k_vec = c()
y_pred = knn(train = diab.train[ , -9],
test = diab.test[ , -9],
cl = diab.train[ , 9],
k = 10)
head(y_pred)## [1] 0 0 1 1 0 0
## Levels: 0 1#Fitting K-NN to the Training set and Predicting the Test set results
vec = c()
k_vec = c()
for (k in 1:50){
y_pred = knn(train = diab.train[ , -9],
test = diab.test[ , -9],
cl = diab.train[ , 9],
k = k)
error = mean(y_pred != diab.test$Outcome) #measure of accuracy
k_vec = c(k_vec, k)
vec = c(vec, error)
}
head(vec)## [1] 0.3051948 0.3376623 0.3116883 0.3441558 0.3051948 0.2922078df.error = data.frame(k_vec, vec)
head(df.error)## k_vec vec
## 1 1 0.3051948
## 2 2 0.3376623
## 3 3 0.3116883
## 4 4 0.3441558
## 5 5 0.3051948
## 6 6 0.2922078Elbow Method
ggplot(df.error,
aes(k_vec, vec)) +
geom_line()
KNN Confusion Matrix
y_pred = knn(train = diab.train[, -9],
test = diab.test[, -9],
cl = diab.train[, 9],
k = 9)
# Making the Confusion Matrix
cm = table(diab.test[, 9], y_pred)
cm## y_pred
## 0 1
## 0 84 16
## 1 23 31confusionMatrix(diab.test[ , 9],
y_pred)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 84 16
## 1 23 31
##
## Accuracy : 0.7468
## 95% CI : (0.6705, 0.8133)
## No Information Rate : 0.6948
## P-Value [Acc > NIR] : 0.09312
##
## Kappa : 0.4268
##
## Mcnemar's Test P-Value : 0.33667
##
## Sensitivity : 0.7850
## Specificity : 0.6596
## Pos Pred Value : 0.8400
## Neg Pred Value : 0.5741
## Prevalence : 0.6948
## Detection Rate : 0.5455
## Detection Prevalence : 0.6494
## Balanced Accuracy : 0.7223
##
## 'Positive' Class : 0
## Kappa: 0.4268
Decision Tree & Random Forest
head(diab.train)## Pregnancies Glucose BloodPressure SkinThickness Insulin BMI
## 1 6 148 72.00000 35.00000 154.3137 33.6
## 2 1 85 66.00000 29.00000 154.3137 26.6
## 3 8 183 64.00000 29.17647 154.3137 23.3
## 4 1 89 66.00000 23.00000 94.0000 28.1
## 5 0 137 40.00000 35.00000 168.0000 43.1
## 8 10 115 72.43027 29.17647 154.3137 35.3
## DiabetesPedigreeFunction Age Outcome
## 1 0.627 50 1
## 2 0.351 31 0
## 3 0.672 32 1
## 4 0.167 21 0
## 5 2.288 33 1
## 8 0.134 29 0head(diab.test)## Pregnancies Glucose BloodPressure SkinThickness Insulin BMI
## 6 5 116 74 29.17647 154.3137 25.6
## 7 3 78 50 32.00000 88.0000 31.0
## 9 2 197 70 45.00000 543.0000 30.5
## 14 1 189 60 23.00000 846.0000 30.1
## 17 0 118 84 47.00000 230.0000 45.8
## 22 8 99 84 29.17647 154.3137 35.4
## DiabetesPedigreeFunction Age Outcome
## 6 0.201 30 0
## 7 0.248 26 1
## 9 0.158 53 1
## 14 0.398 59 1
## 17 0.551 31 1
## 22 0.388 50 0str(diab.train)## 'data.frame': 614 obs. of 9 variables:
## $ Pregnancies : int 6 1 8 1 0 10 8 4 10 10 ...
## $ Glucose : num 148 85 183 89 137 115 125 110 168 139 ...
## $ BloodPressure : num 72 66 64 66 40 ...
## $ SkinThickness : num 35 29 29.2 23 35 ...
## $ Insulin : num 154 154 154 94 168 ...
## $ BMI : num 33.6 26.6 23.3 28.1 43.1 ...
## $ DiabetesPedigreeFunction: num 0.627 0.351 0.672 0.167 2.288 ...
## $ Age : int 50 31 32 21 33 29 54 30 34 57 ...
## $ Outcome : Factor w/ 2 levels "0","1": 2 1 2 1 2 1 2 1 2 1 ...str(diab.test)## 'data.frame': 154 obs. of 9 variables:
## $ Pregnancies : int 5 3 2 1 0 8 11 9 2 0 ...
## $ Glucose : num 116 78 197 189 118 99 143 102 90 180 ...
## $ BloodPressure : num 74 50 70 60 84 84 94 76 68 66 ...
## $ SkinThickness : num 29.2 32 45 23 47 ...
## $ Insulin : num 154 88 543 846 230 ...
## $ BMI : num 25.6 31 30.5 30.1 45.8 35.4 36.6 32.9 38.2 42 ...
## $ DiabetesPedigreeFunction: num 0.201 0.248 0.158 0.398 0.551 ...
## $ Age : int 30 26 53 59 31 50 51 46 27 25 ...
## $ Outcome : Factor w/ 2 levels "0","1": 1 2 2 2 2 1 2 2 2 2 ...sum(is.na(diab.train))## [1] 0sum(is.na(diab.test))## [1] 0Decision Tree
Tree
tree = rpart(formula = Outcome ~ .,
method = "class",
data = diab.train)Tree Prediction
#Predicting the Test Set Results
y_pred = predict(tree,
newdata = diab.test)
head(y_pred)## 0 1
## 6 0.9491525 0.05084746
## 7 0.9298246 0.07017544
## 9 0.1500000 0.85000000
## 14 0.1500000 0.85000000
## 17 0.1666667 0.83333333
## 22 0.9298246 0.07017544y_pred_class = ifelse(y_pred[, "0"] >= 0.5,
0, 1)Tree Confusion Matrix
# Making the Confusion Matrix
cm = table(diab.test$Outcome,
y_pred_class)
cm## y_pred_class
## 0 1
## 0 88 12
## 1 24 30Tree ROC
result.roc = roc(diab.test$Outcome,
y_pred[ ,"0"])## Setting levels: control = 0, case = 1## Setting direction: controls > casesresult.roc##
## Call:
## roc.default(response = diab.test$Outcome, predictor = y_pred[, "0"])
##
## Data: y_pred[, "0"] in 100 controls (diab.test$Outcome 0) > 54 cases (diab.test$Outcome 1).
## Area under the curve: 0.7947plot(result.roc)
Decision Trees
plot(tree,
uniform=TRUE,
main="Diabetes Outcome")
text(tree,
use.n=TRUE,
all=TRUE)
prp(tree)
Random Forest
RF <- randomForest(formula = Outcome ~ .,
method='class',
data = diab.train)
RF##
## Call:
## randomForest(formula = Outcome ~ ., data = diab.train, method = "class")
## Type of random forest: classification
## Number of trees: 500
## No. of variables tried at each split: 2
##
## OOB estimate of error rate: 25.57%
## Confusion matrix:
## 0 1 class.error
## 0 340 60 0.150000
## 1 97 117 0.453271importance(RF)## MeanDecreaseGini
## Pregnancies 23.45711
## Glucose 71.64581
## BloodPressure 24.75545
## SkinThickness 19.84609
## Insulin 22.99613
## BMI 44.23679
## DiabetesPedigreeFunction 32.54496
## Age 37.69331#MeanDecreaseGini --> Importance (IncNodePurity)diab.test1 <- diab.test[-9]
head(diab.test1)## Pregnancies Glucose BloodPressure SkinThickness Insulin BMI
## 6 5 116 74 29.17647 154.3137 25.6
## 7 3 78 50 32.00000 88.0000 31.0
## 9 2 197 70 45.00000 543.0000 30.5
## 14 1 189 60 23.00000 846.0000 30.1
## 17 0 118 84 47.00000 230.0000 45.8
## 22 8 99 84 29.17647 154.3137 35.4
## DiabetesPedigreeFunction Age
## 6 0.201 30
## 7 0.248 26
## 9 0.158 53
## 14 0.398 59
## 17 0.551 31
## 22 0.388 50Random Forest Probabilities
y_prob = predict(RF,
newdata = diab.test1,
type="prob")
head(y_prob)## 0 1
## 6 0.920 0.080
## 7 0.922 0.078
## 9 0.288 0.712
## 14 0.308 0.692
## 17 0.328 0.672
## 22 0.696 0.304Random Forest Prediction
# Predicting the Test set results
y_pred = predict(RF,
newdata = diab.test)confusionMatrix(diab.test[ , 9],
y_pred)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 86 14
## 1 21 33
##
## Accuracy : 0.7727
## 95% CI : (0.6984, 0.8363)
## No Information Rate : 0.6948
## P-Value [Acc > NIR] : 0.02001
##
## Kappa : 0.4856
##
## Mcnemar's Test P-Value : 0.31049
##
## Sensitivity : 0.8037
## Specificity : 0.7021
## Pos Pred Value : 0.8600
## Neg Pred Value : 0.6111
## Prevalence : 0.6948
## Detection Rate : 0.5584
## Detection Prevalence : 0.6494
## Balanced Accuracy : 0.7529
##
## 'Positive' Class : 0
## Clustering
K-Means Clustering
diab.train2 <- diab.train[1:8]
head(diab.train2)## Pregnancies Glucose BloodPressure SkinThickness Insulin BMI
## 1 6 148 72.00000 35.00000 154.3137 33.6
## 2 1 85 66.00000 29.00000 154.3137 26.6
## 3 8 183 64.00000 29.17647 154.3137 23.3
## 4 1 89 66.00000 23.00000 94.0000 28.1
## 5 0 137 40.00000 35.00000 168.0000 43.1
## 8 10 115 72.43027 29.17647 154.3137 35.3
## DiabetesPedigreeFunction Age
## 1 0.627 50
## 2 0.351 31
## 3 0.672 32
## 4 0.167 21
## 5 2.288 33
## 8 0.134 29wcss2 = vector ()
for (i in 1:10){ #range of number of clusters, max limit can be any reasonable number
model = kmeans(diab.train2, i)
wcss2[i] = sum(model$withinss)
}K-Means Find K
wcss = vector()
for (i in 1:10){
print(i)
model = kmeans(diab.train2, i)
wcss[i] = sum(model$withinss)
}## [1] 1
## [1] 2
## [1] 3
## [1] 4
## [1] 5
## [1] 6
## [1] 7
## [1] 8
## [1] 9
## [1] 10plot(1:10,
wcss,
type = "b",
main = paste("The Elbow Method"),
xlab = "Number of Clusters",
ylab = "WCSS")
kmeans = kmeans(x = diab.train2,
centers = 2)
head(kmeans$cluster, 10)## 1 2 3 4 5 8 10 11 12 13
## 1 1 1 2 1 1 1 1 1 1head(kmeans$centers, 10)## Pregnancies Glucose BloodPressure SkinThickness Insulin BMI
## 1 4.057816 127.1758 73.76700 29.84872 178.91355 32.70388
## 2 2.795918 104.6039 68.18367 27.04082 76.16327 31.50011
## DiabetesPedigreeFunction Age
## 1 0.4726959 34.72805
## 2 0.4697143 27.63946wcss = kmeans$withinss
wcss## [1] 3117899.1 258757.9sum(kmeans$withinss)## [1] 3376657head(kmeans$tot.withinss, 10)## [1] 3376657K-Means Clusters
y_kmeans = kmeans$cluster
clusplot(diab.train2,
y_kmeans,
lines = 0,
shade = FALSE,
color = TRUE,
labels = 2,
plotchar = FALSE,
span = TRUE,
main = "Clusters of Patients")
Hierarchical Clustering
hc = hclust(d = dist(diab.train2,
method = "euclidean"),
method = "ward.D") #Variance within each cluster
plot(hc,
main = "Dendrogram",
xlab = "Patients",
ylab = "Euclidean Distances")
y_hc = cutree(hc, 2)
head(y_hc)## 1 2 3 4 5 8
## 1 1 1 1 1 1Hierarchical Clustering Clusters
clusplot(diab.train2,
y_hc,
lines = 0,
shade = FALSE,
color = TRUE,
labels= 2,
plotchar = FALSE,
span = TRUE,
main = 'Clusters of Patients')
Hierarchical Clustering Find K
fviz_nbclust(diab.train2,
hcut,
method = "silhouette") +
labs(subtitle = "Silhouette method")
fviz_nbclust(diab.train2,
hcut,
nstart = 25,
method = "gap_stat",
nboot = 50) +
labs(subtitle = "Gap statistic method")